Publication Date
2003
Journal or Book Title
Mathematics and Computers in Simulation
Abstract
In this paper we investigate the emergence of time-periodic and time quasiperiodic (sometimes infinitely long-lived and sometimes very long-lived or metastable) solutions of discrete nonlinear wave equations: discrete sine Gordon, discrete φ4 and discrete nonlinear Schrödinger equation (DNLS). The solutions we consider are periodic oscillations on a kink or standing wave breather background. The origin of these oscillations is the presence of internal modes, associated with the static ground state. Some of these modes are associated with the breaking of translational invariance, in going from a spatially continuous to a spatially discrete system. Others are associated with discrete modes which bifurcate from the continuous spectrum. It is also possible that such modes exist in the continuum limit and persist in the discrete case. The regimes of existence, stability and metastability of states as the lattice spacing is varied are investigated analytically and numerically. A consequence of our analysis is a class of spatially localized, time quasiperiodic solutions of the discrete nonlinear Schrödinger equation. We demonstrate, however, that this class of quasiperiodic solutions is rather special and that its natural generalizations yield only metastable quasiperiodic solutions.
Pages
65-78
Volume
62
Issue
1-2
Recommended Citation
Kevrekidis, PG, "Breathers on a background: periodic and quasiperiodic solutions of extended discrete nonlinear wave systems" (2003). Mathematics and Computers in Simulation. 1138.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1138
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://dx.doi.org/10.1016/S0378-4754(02)00185-4